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답안 #757470

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
757470 2023-06-13T08:26:53 Z happypotato 메기 농장 (IOI22_fish) C++17
100 / 100
 708 ms 123664 KB 
#include "fish.h"
 
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define pii pair<int, int>
#define ff first
#define ss second
#define pb push_back
#pragma GCC optimize("Ofast")
 
long long max_weights(int32_t n, int32_t m, vector<int32_t> X, vector<int32_t> Y,
					vector<int32_t> W) {
	
	for (int i = 0; i < m; i++) {
		X[i]++; Y[i]++;
	}

	vector<pii> a[n + 1], ps[n + 1];
	vector<int> critpts[n + 1];
	for (int i = 1; i <= n; i++) {
		a[i].pb({0, 0});
		ps[i].pb({0, 0});
		critpts[i].pb(0);
		critpts[i].pb(n);
	}
	for (int i = 0; i < m; i++) {
		a[X[i]].pb({Y[i], W[i]});
		// critical points: (X[i] +- 1, Y[i]), (X[i], Y[i] - 1)
		if (X[i] > 1) {
			critpts[X[i] - 1].pb(Y[i]);
		}
		if (X[i] < n) {
			critpts[X[i] + 1].pb(Y[i]);
		}
		critpts[X[i]].pb(Y[i] - 1);
	}
	for (int i = 1; i <= n; i++) {
		sort(a[i].begin(), a[i].end());
		for (pii &x : a[i]) {
			ps[i].pb({x.ff, ps[i].back().ss + x.ss});
		}
	}
 
	function<int(int, int)> GetPS = [&](int x, int y) -> int {
		int lb = 0, rb = (int)(ps[x].size()) - 1;
		while (lb < rb) {
			int mid = (lb + rb + 1) >> 1;
			if (ps[x][mid].ff <= y) lb = mid;
			else rb = mid - 1;
		}
		return ps[x][lb].ss;
	};

	// O(n^2): dp[increasing][pos][height] = max ans from 1 to [pos] with [pos] getting [height], height must be [increasing]
 
	vector<vector<pii>> dp[2];
	dp[0].resize(n + 1); dp[1].resize(n + 1);
	for (int i = 0; i <= n; i++) {
		dp[0][0].pb({i, (i == 0 ? 0 : -1e18)});
		dp[1][0].pb({i, (i == 0 ? 0 : -1e18)});
		
		dp[0][1].pb({i, 0});
		dp[1][1].pb({i, 0});
	}
	for (int i = 2; i <= n; i++) {
		sort(critpts[i].begin(), critpts[i].end());
		for (int &x : critpts[i]) {
			if (!dp[0][i].empty() && x == dp[0][i].back().ff) continue;
			dp[0][i].pb({x, 0});
			dp[1][i].pb({x, 0});
		}
	}
	vector<pii> cur;
	int ptr = 0, curans = 0;

	for (int i = 2; i <= n; i++) {

		// Case 0: height of i is 0
		
		// dp[flag][i][0].ff is always 0
		for (int j = 0; j < (int)(dp[0][i - 1].size()); j++) {
			dp[0][i][0].ss = max(dp[0][i][0].ss, max(dp[0][i - 1][j].ss, dp[1][i - 1][j].ss) + GetPS(i, dp[0][i - 1][j].ff));
		}
		dp[1][i][0].ss = dp[0][i][0].ss;
		
		// Case 1: height of i-1 is 0
		// Case 1.1: height of i-2 <= height of i
		
		cur.clear();
		for (int j = 0; j < (int)(dp[0][i - 2].size()); j++) {
			cur.pb({dp[0][i - 2][j].ff, max(dp[0][i - 2][j].ss, dp[1][i - 2][j].ss)});
		}
		for (int j = 1; j < (int)(cur.size()); j++) {
			cur[j].ss = max(cur[j].ss, cur[j - 1].ss);
		}
		ptr = 0; curans = 0;
		for (int j = 0; j < (int)(dp[0][i].size()); j++) {
			while (ptr < (int)(cur.size()) && cur[ptr].ff <= dp[0][i][j].ff) {
				curans = max(curans, cur[ptr].ss);
				ptr++;
			}
			dp[0][i][j].ss = max(dp[0][i][j].ss, curans + GetPS(i - 1, dp[0][i][j].ff));
			dp[1][i][j].ss = max(dp[1][i][j].ss, curans + GetPS(i - 1, dp[0][i][j].ff));
		}
 
		// Case 1.2: height of i-2 >= height of i
		
		cur.clear();
		for (int j = 0; j < (int)(dp[0][i - 2].size()); j++) {
			cur.pb({dp[0][i - 2][j].ff, max(dp[0][i - 2][j].ss, dp[1][i - 2][j].ss) + GetPS(i - 1, dp[0][i - 2][j].ff)});
		}
		for (int j = (int)(cur.size()) - 2; j >= 0; j--) {
			cur[j].ss = max(cur[j].ss, cur[j + 1].ss);
		}
		ptr = (int)(cur.size()) - 1; curans = 0;
		for (int j = (int)(dp[0][i].size()) - 1; j >= 0; j--) {
			while (ptr >= 0 && cur[ptr].ff >= dp[0][i][j].ff) {
				curans = max(curans, cur[ptr].ss);
				ptr--;
			}
			dp[0][i][j].ss = max(dp[0][i][j].ss, curans);
			dp[1][i][j].ss = max(dp[1][i][j].ss, curans);
		}
 
		// now height of i-1 > 0
		// Case 2: height of i-1 <= height of i
		
		cur.clear();
		ptr = 1; curans = 0;
		for (int j = 1; j < (int)(dp[0][i].size()); j++) {
			curans += (GetPS(i - 1, dp[0][i][j].ff) - GetPS(i - 1, (j == 1 ? 1 : dp[0][i][j - 1].ff)));
			while (ptr < (int)(dp[0][i - 1].size()) && dp[0][i - 1][ptr].ff <= dp[0][i][j].ff) {
				curans = max(curans, dp[0][i - 1][ptr].ss + (GetPS(i - 1, dp[0][i][j].ff) - GetPS(i - 1, dp[0][i - 1][ptr].ff)));
				ptr++;
			}
			dp[0][i][j].ss = max(dp[0][i][j].ss, curans);
		}
 
		// Case 3: height of i-1 >= height of i
 
		cur.clear();
		ptr = (int)(dp[1][i - 1].size()) - 1; curans = 0;
		for (int j = (int)(dp[1][i].size()) - 1; j >= 1; j--) {
			curans += (GetPS(i, (j + 1 == (int)(dp[1][i].size()) ? n : dp[1][i][j + 1].ff)) - GetPS(i, dp[1][i][j].ff));
			while (ptr >= 0 && dp[1][i - 1][ptr].ff >= dp[0][i][j].ff) {
				curans = max(curans, max(dp[0][i - 1][ptr].ss, dp[1][i - 1][ptr].ss) + (GetPS(i, dp[1][i - 1][ptr].ff) - GetPS(i, dp[1][i][j].ff)));
				ptr--;
			}
			dp[1][i][j].ss = max(dp[1][i][j].ss, curans);
		}
	}
 
	int ans = 0;
	for (pii &x : dp[0][n]) ans = max(ans, x.ss);
	for (pii &x : dp[1][n]) ans = max(ans, x.ss);
	return ans;
}
 
#undef int

Subtask #1
3.0 / 3.0

# 결과 실행 시간 메모리 Grader output
1 Correct 166 ms 50980 KB Output is correct
2 Correct 197 ms 57280 KB Output is correct
3 Correct 90 ms 44828 KB Output is correct
4 Correct 86 ms 44820 KB Output is correct
5 Correct 573 ms 109300 KB Output is correct
6 Correct 660 ms 123664 KB Output is correct

Subtask #2
6.0 / 6.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 265 ms 61596 KB Output is correct
3 Correct 317 ms 69900 KB Output is correct
4 Correct 157 ms 50992 KB Output is correct
5 Correct 183 ms 57192 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 1 ms 300 KB Output is correct
9 Correct 1 ms 296 KB Output is correct
10 Correct 91 ms 44820 KB Output is correct
11 Correct 93 ms 44776 KB Output is correct
12 Correct 208 ms 54140 KB Output is correct
13 Correct 234 ms 61140 KB Output is correct
14 Correct 194 ms 52680 KB Output is correct
15 Correct 210 ms 56148 KB Output is correct
16 Correct 206 ms 52768 KB Output is correct
17 Correct 226 ms 57956 KB Output is correct

Subtask #3
9.0 / 9.0

# 결과 실행 시간 메모리 Grader output
1 Correct 93 ms 44828 KB Output is correct
2 Correct 88 ms 44840 KB Output is correct
3 Correct 171 ms 51288 KB Output is correct
4 Correct 190 ms 52472 KB Output is correct
5 Correct 239 ms 63092 KB Output is correct
6 Correct 272 ms 62472 KB Output is correct
7 Correct 235 ms 63024 KB Output is correct
8 Correct 240 ms 63120 KB Output is correct

Subtask #4
14.0 / 14.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 296 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 300 KB Output is correct
6 Correct 1 ms 300 KB Output is correct
7 Correct 0 ms 304 KB Output is correct
8 Correct 1 ms 300 KB Output is correct
9 Correct 2 ms 440 KB Output is correct
10 Correct 3 ms 872 KB Output is correct
11 Correct 2 ms 468 KB Output is correct
12 Correct 2 ms 596 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 2 ms 596 KB Output is correct

Subtask #5
21.0 / 21.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 296 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 300 KB Output is correct
6 Correct 1 ms 300 KB Output is correct
7 Correct 0 ms 304 KB Output is correct
8 Correct 1 ms 300 KB Output is correct
9 Correct 2 ms 440 KB Output is correct
10 Correct 3 ms 872 KB Output is correct
11 Correct 2 ms 468 KB Output is correct
12 Correct 2 ms 596 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 2 ms 596 KB Output is correct
15 Correct 1 ms 468 KB Output is correct
16 Correct 3 ms 724 KB Output is correct
17 Correct 62 ms 8636 KB Output is correct
18 Correct 54 ms 9164 KB Output is correct
19 Correct 46 ms 8984 KB Output is correct
20 Correct 47 ms 8436 KB Output is correct
21 Correct 49 ms 8364 KB Output is correct
22 Correct 99 ms 16560 KB Output is correct
23 Correct 16 ms 2616 KB Output is correct
24 Correct 47 ms 6524 KB Output is correct
25 Correct 2 ms 596 KB Output is correct
26 Correct 13 ms 2516 KB Output is correct

Subtask #6
17.0 / 17.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 296 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 300 KB Output is correct
6 Correct 1 ms 300 KB Output is correct
7 Correct 0 ms 304 KB Output is correct
8 Correct 1 ms 300 KB Output is correct
9 Correct 2 ms 440 KB Output is correct
10 Correct 3 ms 872 KB Output is correct
11 Correct 2 ms 468 KB Output is correct
12 Correct 2 ms 596 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 2 ms 596 KB Output is correct
15 Correct 1 ms 468 KB Output is correct
16 Correct 3 ms 724 KB Output is correct
17 Correct 62 ms 8636 KB Output is correct
18 Correct 54 ms 9164 KB Output is correct
19 Correct 46 ms 8984 KB Output is correct
20 Correct 47 ms 8436 KB Output is correct
21 Correct 49 ms 8364 KB Output is correct
22 Correct 99 ms 16560 KB Output is correct
23 Correct 16 ms 2616 KB Output is correct
24 Correct 47 ms 6524 KB Output is correct
25 Correct 2 ms 596 KB Output is correct
26 Correct 13 ms 2516 KB Output is correct
27 Correct 6 ms 2160 KB Output is correct
28 Correct 299 ms 37880 KB Output is correct
29 Correct 405 ms 52716 KB Output is correct
30 Correct 530 ms 86500 KB Output is correct
31 Correct 539 ms 85976 KB Output is correct
32 Correct 343 ms 51536 KB Output is correct
33 Correct 538 ms 86624 KB Output is correct
34 Correct 529 ms 86460 KB Output is correct
35 Correct 169 ms 27748 KB Output is correct
36 Correct 507 ms 70904 KB Output is correct

Subtask #7
14.0 / 14.0

# 결과 실행 시간 메모리 Grader output
1 Correct 93 ms 44828 KB Output is correct
2 Correct 88 ms 44840 KB Output is correct
3 Correct 171 ms 51288 KB Output is correct
4 Correct 190 ms 52472 KB Output is correct
5 Correct 239 ms 63092 KB Output is correct
6 Correct 272 ms 62472 KB Output is correct
7 Correct 235 ms 63024 KB Output is correct
8 Correct 240 ms 63120 KB Output is correct
9 Correct 297 ms 62900 KB Output is correct
10 Correct 153 ms 34808 KB Output is correct
11 Correct 355 ms 69440 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 1 ms 212 KB Output is correct
15 Correct 1 ms 212 KB Output is correct
16 Correct 1 ms 296 KB Output is correct
17 Correct 0 ms 212 KB Output is correct
18 Correct 93 ms 44872 KB Output is correct
19 Correct 88 ms 44820 KB Output is correct
20 Correct 98 ms 44840 KB Output is correct
21 Correct 92 ms 44776 KB Output is correct
22 Correct 336 ms 69596 KB Output is correct
23 Correct 383 ms 81660 KB Output is correct
24 Correct 394 ms 82492 KB Output is correct

Subtask #8
16.0 / 16.0

# 결과 실행 시간 메모리 Grader output
1 Correct 166 ms 50980 KB Output is correct
2 Correct 197 ms 57280 KB Output is correct
3 Correct 90 ms 44828 KB Output is correct
4 Correct 86 ms 44820 KB Output is correct
5 Correct 573 ms 109300 KB Output is correct
6 Correct 660 ms 123664 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 265 ms 61596 KB Output is correct
9 Correct 317 ms 69900 KB Output is correct
10 Correct 157 ms 50992 KB Output is correct
11 Correct 183 ms 57192 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 1 ms 300 KB Output is correct
15 Correct 1 ms 296 KB Output is correct
16 Correct 91 ms 44820 KB Output is correct
17 Correct 93 ms 44776 KB Output is correct
18 Correct 208 ms 54140 KB Output is correct
19 Correct 234 ms 61140 KB Output is correct
20 Correct 194 ms 52680 KB Output is correct
21 Correct 210 ms 56148 KB Output is correct
22 Correct 206 ms 52768 KB Output is correct
23 Correct 226 ms 57956 KB Output is correct
24 Correct 93 ms 44828 KB Output is correct
25 Correct 88 ms 44840 KB Output is correct
26 Correct 171 ms 51288 KB Output is correct
27 Correct 190 ms 52472 KB Output is correct
28 Correct 239 ms 63092 KB Output is correct
29 Correct 272 ms 62472 KB Output is correct
30 Correct 235 ms 63024 KB Output is correct
31 Correct 240 ms 63120 KB Output is correct
32 Correct 1 ms 212 KB Output is correct
33 Correct 1 ms 296 KB Output is correct
34 Correct 1 ms 212 KB Output is correct
35 Correct 1 ms 212 KB Output is correct
36 Correct 1 ms 300 KB Output is correct
37 Correct 1 ms 300 KB Output is correct
38 Correct 0 ms 304 KB Output is correct
39 Correct 1 ms 300 KB Output is correct
40 Correct 2 ms 440 KB Output is correct
41 Correct 3 ms 872 KB Output is correct
42 Correct 2 ms 468 KB Output is correct
43 Correct 2 ms 596 KB Output is correct
44 Correct 1 ms 340 KB Output is correct
45 Correct 2 ms 596 KB Output is correct
46 Correct 1 ms 468 KB Output is correct
47 Correct 3 ms 724 KB Output is correct
48 Correct 62 ms 8636 KB Output is correct
49 Correct 54 ms 9164 KB Output is correct
50 Correct 46 ms 8984 KB Output is correct
51 Correct 47 ms 8436 KB Output is correct
52 Correct 49 ms 8364 KB Output is correct
53 Correct 99 ms 16560 KB Output is correct
54 Correct 16 ms 2616 KB Output is correct
55 Correct 47 ms 6524 KB Output is correct
56 Correct 2 ms 596 KB Output is correct
57 Correct 13 ms 2516 KB Output is correct
58 Correct 6 ms 2160 KB Output is correct
59 Correct 299 ms 37880 KB Output is correct
60 Correct 405 ms 52716 KB Output is correct
61 Correct 530 ms 86500 KB Output is correct
62 Correct 539 ms 85976 KB Output is correct
63 Correct 343 ms 51536 KB Output is correct
64 Correct 538 ms 86624 KB Output is correct
65 Correct 529 ms 86460 KB Output is correct
66 Correct 169 ms 27748 KB Output is correct
67 Correct 507 ms 70904 KB Output is correct
68 Correct 297 ms 62900 KB Output is correct
69 Correct 153 ms 34808 KB Output is correct
70 Correct 355 ms 69440 KB Output is correct
71 Correct 1 ms 212 KB Output is correct
72 Correct 1 ms 212 KB Output is correct
73 Correct 1 ms 212 KB Output is correct
74 Correct 1 ms 212 KB Output is correct
75 Correct 1 ms 296 KB Output is correct
76 Correct 0 ms 212 KB Output is correct
77 Correct 93 ms 44872 KB Output is correct
78 Correct 88 ms 44820 KB Output is correct
79 Correct 98 ms 44840 KB Output is correct
80 Correct 92 ms 44776 KB Output is correct
81 Correct 336 ms 69596 KB Output is correct
82 Correct 383 ms 81660 KB Output is correct
83 Correct 394 ms 82492 KB Output is correct
84 Correct 679 ms 95960 KB Output is correct
85 Correct 708 ms 100876 KB Output is correct
86 Correct 616 ms 114328 KB Output is correct
87 Correct 647 ms 119904 KB Output is correct
88 Correct 1 ms 212 KB Output is correct
89 Correct 682 ms 119836 KB Output is correct
90 Correct 535 ms 108732 KB Output is correct
91 Correct 401 ms 98452 KB Output is correct